Redshift distribution of velocity dispersion (σ, left panel) and rotational support (V/σ, right panel) for our extended sample (colored markers) consisting of massive galaxies. The σ and V/σ values are derived using emission lines tracing cold gas (i.e., CO, [CI], [CII]). The pink solid lines show the best-fit empirical relations, with the 1-σ uncertainties (dark pink area) and the intrinsic scatter (pink area).